Let x0 of type (ι → ο) → ο be given.

Let x1 of type ((ι → ο) → ο) → ο be given.

Assume H0: x1 x0.

Let x2 of type ο be given.

Assume H1: ∀ x3 : (ι → ο) → ο . and (a4b00.. x0 = a4b00.. x3) (x1 x3) ⟶ x2.

Apply H1 with x0.

Apply unknownprop_389e2fb1855352fcc964ea44fe6723d7a1c2d512f04685300e3e97621725b977 with a4b00.. x0 = a4b00.. x0, x1 x0 leaving 2 subgoals.

Let x3 of type (((ι → ο) → ο) → ο) → (((ι → ο) → ο) → ο) → ο be given.

Assume H2: x3 (a4b00.. x0) (a4b00.. x0).

The subproof is completed by applying H2.

The subproof is completed by applying H0.

■

Proofgold Proof